To compute the distribution function when the characteristic function is known

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Abstract
1. Introduction In this paper we are going to study the effect of multiplying the characteristic function by a certain function which is identically zero outside a finite interval. The main purpose is to keep control of numerical integration of characteristic functions in order to determine the corresponding distribution function. The difficulties connected with such integration arise from the fact that the integral is approximated with the aid of a finite number of values of the integrand, chosen in a finite interval, and that no general methods are available to estimate the effect of disregarding the “tails”. Even if the method to be described in this paper is primarily intended for numerical integration it seems plausible that it can also be used in other connections.

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